Elliptic curve isogeny class 121.1-b over number field \(\Q(\sqrt{22}) \)

• Base field: \(\Q(\sqrt{22}) \)
• Label: 2.2.88.1-121.1-b
• Conductor: 121.1
• Rank bounds: 0...1

Base field \(\Q(\sqrt{22}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 22 \); class number \(1\).

Elliptic curves in class 121.1-b over \(\Q(\sqrt{22}) \)

Isogeny class 121.1-b contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
121.1-b1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -30\) , \( -76\bigr] \)
121.1-b2	\( \bigl[a + 1\) , \( a\) , \( a\) , \( 41720 a - 195643\) , \( -39280465 a + 184241784\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph